True, though you have to include the stock market too, that's equity. US Bond market cap is roughly $120 trillion, stock market cap is ~$45trillion. So the equity market is about half the debt market, if you exclude govt debt.

That said, if somehow you had a similar hypothetical economy but with little or no debt, the equity side might be larger.

Vast majority of stock market cap does not contribute to company capitalization. Primary equity offerings on the market are rare and use only a fraction of total equity. Most trades are secondary and don’t capitalize the company. The entire bond market value is a capital raise for the companies.